Question

Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts?

(A) The function f(x) has a higher y-intercept.

(B) The function g(x) has a higher y-intercept.

(C) They both have the same y-intercept.

(D) The relationship between y-intercepts cannot be determined.

Answer 1

we have that

`f(x)=4x-1`

In the table

Let

`A(1,3)\\B(4,6)\\C(7,9)`

Step
`1`

Find the equation of the line of g(x)

Find the slope AB

slope m is equal to

`m=((y2-y1))/((x2-x1))`

`m=((6-3))/((4-1))`

`m=1`

with the slope m and the point
`A(1,3)` find the equation of the line

`y-y1=m(x-x1)`

`y-3=1*(x-1)`

`y=x-1+3`

`y=x+2`

`g(x)=x+2`

Step
`2`

Find the y-intercept of f(x) and g(x)

we know that

the y-intercept is the value of the y-coordinate when the value of x is equal to zero

`f(x)=4x-1`

for
`x=0`

`f(x)=4*0-1`

`f(x)=-1`

the y-intercept of f(x) is equal to
`-1`

`g(x)=x+2`

for
`x=0`

`g(x)=0+2`

`g(x)=2`

the y-intercept of g(x) is equal to
`2`

therefore

the answer is the option

(B) The function g(x) has a higher y-intercept

Answer 2

f(x) = 4x-1, so the y-intercept is 4(0)-1 = -1
g(x) = x+2, so the y-intercept is (0)+2= 2
(B) The function g(x) has a higher y-intercept.